A. K&K Pharmaceuticals, a major drug company, is bringing to market a new rheumatoid arthritis medication. The company claims that on average 94 percent of the patients it tested with this drug did not experience nausea, the only known side effect of this drug. Twenty one volunteers were randomly chosen to participate in independent clinical trials conducted for the US Food and Drug Administration. Assume that patients' reactions to the drug are independent of each other.
1. How many of the 21 test patients should be expected to experience nausea after taking this drug?
2. What is the chance that none of the test patients will be nauseas after taking this drug?
3. What is the chance that one and only one of the test patients will be nauseas after taking this drug?
4. What is the chance that more than one of the test patients is nauseas after taking this drug?
5. What is the chance that after taking the drug, fewer of these patients than expected are nauseas?
6. Suppose that of 21 test patients, five patients actually do experience nausea. What is the chance that exactly five of the 21 patients experience nausea?
7. In another study to determine the clinical reason for the nausea, the researchers expect to need thirteen patients to get nauseas after taking the drug. How many volunteer patients do the researchers need to choose to participate in this study?